Single correct option
A boat covers 21 km upstream and 65 km downstream in 8 hours. It covers 49 km upstream and 26 km downstream in 9 hours. What is the speed of the stream?
- A. 2.5 km/h
- B. 3 km/h
- C. 3.5 km/h
- D. 4 km/h
Show answer and solution
Answer: (B) 3 km/h
Let the upstream speed be U and the downstream speed D. Put u = 1/U and d = 1/D:
21u + 65d = 8 … (i)
49u + 26d = 9 … (ii)
Multiply (i) by 26 and (ii) by 65: 546u + 1690d = 208; 3185u + 1690d = 585. Subtracting, 2639u = 377, so u = 1/7, giving U = 7 km/h. Then from (i): 21(1/7) + 65d = 8 → 3 + 65d = 8 → d = 1/13, so D = 13 km/h.
Stream speed = (D − U)/2 = (13 − 7)/2 = 3 km/h.
21u + 65d = 8 … (i)
49u + 26d = 9 … (ii)
Multiply (i) by 26 and (ii) by 65: 546u + 1690d = 208; 3185u + 1690d = 585. Subtracting, 2639u = 377, so u = 1/7, giving U = 7 km/h. Then from (i): 21(1/7) + 65d = 8 → 3 + 65d = 8 → d = 1/13, so D = 13 km/h.
Stream speed = (D − U)/2 = (13 − 7)/2 = 3 km/h.
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